Let and be any three events in a sample space .

MATHEMATICS · Multi-part · A Level · Mathematics · Probability · Probability

Problem

Let

A,\,B

and

C

be any three events in a sample space

S

. (a) Starting from the axioms of probability, derive the formula

P(A\cup B)=P(A)+P(B)-P(A\cap B)

for two events. (b) Using a similar approach, derive an expression for

P(A\cup B\cup C)

in terms of the probabilities of single events, pairwise intersections and the triple intersection. (c) If

A

and

B

are mutually exclusive while

C

is any event, rewrite the expression obtained in part (ii) and interpret each term in the context of mutually exclusive events.